*Average Carbon Flux vs. Segmented Average Carbon Flux*

The value of carbon flux is directly related to carburizing pressure, carburizing temperature, and material properties [24]. In process design, the average carbon flux (mass increment detection after carburizing for 120 s or longer) is measured. Herein, the cylindrical samples are carburized for 30, 60, 90, and 120 s, and are subsequently weighed. Different from typical carbon flux measurement, the carbon flux of the samples at different times of carburization is calculated separately and defined as the segmented average carbon flux (*Je*), as shown in Equation (2).

$$J\_{\text{ef}} = \frac{\Delta m}{\text{S} \cdot \Delta t}.\tag{2}$$

High alloy materials are more likely to absorb carbon atoms. To better determine the accuracy of the original carbon flux model, a carburizing experiment was performed on 16Cr3NiWMoVNbE steel at a carburizing temperature of 920 ◦C and carburizing pressure of 300 Pa. The average carbon flux over 120 s and the segmented average carbon flux were measured. The obtained carbon flux over carburizing time is shown in Figure 1.

Figure 1 shows that the average carbon flux and segmented average carbon flux both decrease as carburizing time increases. During carburization, the carbon concentration gradient at the carburized layer gradually decreases; hence, the number of carbon atoms entering the sample surface per unit time decreases. In the initial stage of carburization from 0 to 60 s, the carbon concentration gradient at the gas–solid interface is relatively large. After 30 s, the carbon flux obtained using the segmented average method is 2.5 times that of the carbon flux obtained by the overall average method, which result in the obtained value exceeding the carbide standard in the carburized layer.

Herein, two carbon flux models using the average carbon flux and segmented average carbon flux are used to calculate the carburizing process; the corresponding results are shown in Figure 2. The number of carburizing pulses is 19 according to both models. As carburizing proceeds,

the carburizing time gradually decreases, and the diffusion time gradually increases. Carburizing stops once the surface carbon concentration reaches 1.3%, and then restarts once the concentration reaches 1.1% through diffusion. For the last pulse, the surface carbon concentration decreases to 0.9%, and the carbon concentration at 1.1 mm of the carburized layer increases to 0.42%. The carburizing process is then completed. The total carburizing time is 18,500 s.

**Figure 1.** Variation in carbon flux with carburizing time.

**Figure 2.** Process curves of (**a**) the average carbon flux method and (**b**) the segmented average carbon flux method.

The changes in surface carbon concentration over carburizing time and boost time along with the number of pulses obtained from the simulations using average carbon flux and segmented average carbon flux are shown in Figures 3 and 4, respectively.

**Figure 3.** First three pulse curves obtained via different carbon flux measurement methods.

**Figure 4.** Carburizing time of each pulse obtained via different carbon flux measurement methods.

Using the average carbon flux model, the pulse time of the first boost stage is 80 s, and the pulse time of boost stages thereafter (2nd–19th) is 14 s. However, the data obtained using the segmented average carbon flux method shows that the first boost had a pulse time of 37 s, and the boost stages thereafter (2nd–19th) had a pulse time of 11 s. The carburizing time of the first boost pulse obtained using the average carbon flux method is 2.2 times longer than the segmented average carbon method. For subsequent pulse times, the first boost pulse obtained using the average carbon flux method is 1.3 times longer than the segmented average carbon method.

The variation in the different boost times will cause differences in the carbide morphology of the carburized layer. The results of carburized layer organization after the different carburizing processes (carburizing and quenching) are shown in Figure 5. For the same diffusion time, the surface organization of the carburized layer obtained using the average carbon flux model appears to have a discontinuous carbide network and some continuous carbide network, whereas the surface organization obtained using the segmented carbon flux model has more diffused carbides, which verifies the efficiency of the proposed model and enables a more accurate and efficient characterization of the actual carbon flux value, effectively avoiding the effects of the first pulse and achieving more precise control over the time of subsequent pulses.

**Figure 5.** Surface organization of carburized layer of 16Cr3NiWMoVNbE steel under (**a**) the average carbon flux model and (**b**) the segmented average carbon flux model after carburizing and quenching.

Based on this influencing factor, a systematic study on the carbon flux model with different materials, carburizing temperature, and carburizing pressure conditions was conducted to determine the effect of the different process conditions on carbon flux and to build a mathematical model for carbon flux.
